Final answer:
A difference in mean rating of -2.3 or less occurring only 5 out of 200 times indicates the difference is statistically significant. Therefore, there is convincing evidence that detergent a is more effective than detergent b.
Step-by-step explanation:
To determine if there is convincing evidence that one detergent is better than the other using a dotplot and the difference in mean ratings from the samples, we need to look at the significance level and the frequency of occurrence of the observed difference.
If a difference in mean rating of – 2.3 or less occurred only 5 out of 200 times, this means that such an extreme or more extreme difference would happen by chance only 5 out of 200 times, or 2.5% of the time, which is less than the commonly used significance level of 5%. Therefore, we would consider this difference to be statistically significant.
The correct answer is: A. Yes, because a difference in mean rating of – 2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that a is more effective than b.